Abstract Symmetry is key in solving many scientific and engineering problems. Drawing on examples from chemical engineering, this chapter illustrates how recognizing fractal scaling and other invariant patterns that envelop multiple scales is an excellent way to bridge multi-scale gaps. Such invariants are frequently observed in biological systems, which are only able to function thanks to the conservation of microscopic properties up to macroscopic scales in a scale-free way. Similarly, by imposing such invariant distributions in engineering designs, the advantages of microscopic (micro- or nanoscale) designs are preserved for macro-scale applications, while considerably reducing complexity and increasing efficiency. This holistic view helps to simplify multi-scale problems, and is proposed as a useful supplement to atomistic, bottom-up approaches.
Panagiotis TrogadasMarc‐Olivier Coppens
Vincent GerbaudCatherine XuerebMarc‐Olivier Coppens
Vincent GerbaudNataliya ShcherbakovaSergio da Cunha
Mas’udah Mas’udahSandra SantosaPavel LivotovArun Prasad Chandra SekaranLuchis Rubianto